Triangular-hexagonal duoprismatic prism

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Triangular-hexagonal duoprismatic prism
Rank5
TypeUniform
Notation
Bowers style acronymTrahip
Coxeter diagramx x3o x6o
Elements
Tera6 triangular-square duoprisms, 2 triangular-hexagonal duoprisms, 3 square-hexagonal duoprisms
Cells6+12 triangular prisms, 18 cubes, 3+6 hexagonal prisms
Faces12 triangles, 18+18+36 squares, 6 hexagons
Edges18+36+36
Vertices36
Vertex figureDigonal disphenoidal pyramid, edge lengths 1 (disphenoid base 1), 3 (disphenoid base 2), 2 (remaining edges)
Measures (edge length 1)
Circumradius
Hypervolume
Diteral anglesTisdip–trip–tisdip: 120°
 Thiddip–trip–tisdip: 90°
 Shiddip–cube–tisdip: 90°
 Thiddip–hip–shiddip: 90°
 Shiddip–hip–shiddip: 60°
HeightsThiddip atop thiddip: 1
 Hip atop shiddip:
Central density1
Number of external pieces11
Level of complexity30
Related polytopes
ArmyTrahip
RegimentTrahip
DualTriangular-hexagonal duotegmatic tegum
ConjugateTriangular-hexagonal duoprismatic prism
Abstract & topological properties
Euler characteristic2
OrientableYes
Properties
SymmetryA2×G2×A1, order 144
ConvexYes
NatureTame

The triangular-hexagonal duoprismatic prism or trahip, also known as the triangular-hexagonal prismatic duoprism, is a convex uniform duoprism that consists of 2 triangular-hexagonal duoprisms, 3 square-hexagonal duoprisms, and 6 triangular-square duoprisms. Each vertex joins 2 triangular-square duoprisms, 2 square-hexagonal duoprisms, and 1 triangular-hexagonal duoprism. Being a prism based on an orbiform polytope, it is also a convex segmentoteron.

Vertex coordinates[edit | edit source]

The vertices of a triangular-hexagonal duoprismatic prism of edge length 1 are given by:

Representations[edit | edit source]

A triangular-pentagonal duoprismatic prism has the following Coxeter diagrams:

  • x x3o x6o (full symmetry)
  • x x3o x3x (hexagons as ditrigons)
  • xx3oo xx6oo&#x (triangular-hexagonal duoprism atop triangular-hexagonal duoprism)
  • xx3oo xx3xx&#x
  • ox xx xx6oo&#x (hexagonal prism atop square-hexagonal duoprism)
  • ox xx xx3xx&#x
  • xxx xxx3xxx&#x

External links[edit | edit source]